Application of FuzzyEn algorithm to the analysis of complexity of chaotic sequence

Abstract

To analyze the complexity of chaotic sequence correctly, complexity of systems, including typical discrete chaotic systems and continuous chaotic systems, are investigated based on the FuzzyEn algorithm. Compared with ApEn, SampEn and Intensive statistical complexity algorithm, the FuzzyEn algorithm is an effective measure algorithm for analyzing chaotic sequence complexity, and it has low sensitivity to and slight dependences on phase space dimension (m), similar tolerance (r) and sequence length (N), better robustness and measure value continuities. Results of the complexities of chaotic systems show that the complexity of continuous chaotic systems are much smaller than those of the discrete chaotic systems. However, having been disturbed by high complex discrete chaotic pseudo-random sequences or classical m-series, the pseudo-random sequences of continuous chaotic systems increase their complexities significantly. Our result provides a theoretical basis for the application of chaotic sequences to the field of cryptography and secure communication.